standard_fit Namespace Reference

Functions
def	distance (x, C, N)
def	function (x, C, N)
def	projection (x, C, N)
def	standard_fit (X)

Variables
list	__all__ = ['standard_fit', 'projection', 'distance', 'function']
string	__author__ = 'Alisue (lambdalisue@hashnote.net)'
string	__date__ = '2013-10-28'
string	__version__ = '0.1.0'

Function Documentation

def standard_fit.distance	(		x,
			C,
			N
	)

Calculate an orthogonal distance between the points and the standard

Args:
    x: n x m dimensional matrix
    C: n dimensional vector whicn indicate the centroid of the standard
    N: n dimensional vector which indicate the normal vector of the standard

Returns:
    m dimensional vector which indicate the orthogonal disntace. the value
    will be negative if the points beside opposite side of the normal vector

Definition at line 74 of file standard_fit.py.

def standard_fit.function	(		x,
			C,
			N
	)

Calculate an orthogonal projection of the points on the standard

Args:
    x: (n-1) x m dimensional matrix
    C: n dimensional vector whicn indicate the centroid of the standard
    N: n dimensional vector which indicate the normal vector of the standard

Returns:
    m dimensional vector which indicate the last attribute value of
    orthogonal projection

Definition at line 89 of file standard_fit.py.

def standard_fit.projection	(		x,
			C,
			N
	)

Create orthogonal projection matrix of x on the plane

Args:
    x: n x m dimensional matrix
    C: n dimensional vector whicn indicate the centroid of the standard
    N: n dimensional vector which indicate the normal vector of the standard

Returns:
    n x m dimensional matrix which indicate the orthogonal projection points
    on the plane

Definition at line 55 of file standard_fit.py.

def standard_fit.standard_fit

(

X

)

Find (n - 1) dimensional standard (e.g. line in 2 dimension, plane in 3
dimension, hyperplane in n dimension) via solving Singular Value
Decomposition.

The idea was explained in the following references

- http://www.caves.org/section/commelect/DUSI/openmag/pdf/SphereFitting.pdf
- http://www.geometrictools.com/Documentation/LeastSquaresFitting.pdf
- http://www.ime.unicamp.br/~marianar/MI602/material%20extra/svd-regression-analysis.pdf
- http://www.ling.ohio-state.edu/~kbaker/pubs/Singular_Value_Decomposition_Tutorial.pdf

Example:
    >>> XY = [[0, 1], [3, 3]]
    >>> XY = np.array(XY)
    >>> C, N = standard_fit(XY)
    >>> C
    array([ 1.5,  2. ])
    >>> N
    array([-0.5547002 ,  0.83205029])

Args:
    X: n x m dimensional matrix which n indicate the number of the dimension
        and m indicate the number of points

Returns:
    [C, N] where C is a centroid vector and N is a normal vector

Definition at line 15 of file standard_fit.py.

Variable Documentation

list standard_fit.__all__ = ['standard_fit', 'projection', 'distance', 'function']

private

Definition at line 11 of file standard_fit.py.

string standard_fit.__author__ = 'Alisue (lambdalisue@hashnote.net)'

private

Definition at line 8 of file standard_fit.py.

string standard_fit.__date__ = '2013-10-28'

private

Definition at line 10 of file standard_fit.py.

string standard_fit.__version__ = '0.1.0'

private

Definition at line 9 of file standard_fit.py.